We're singing "Sherburne" in my chorus for our upcoming fall concert, and it's very different from other 18th century music we've sung! (E.g. Mozart.) According to the Wiki page for Daniel Read,
While the classical music era was in its heyday in Europe, American composers of "serious" music were setting hymn tunes in three- and four-part a cappella style, with simple folklike melodies and little regard for functional harmony.
Why were the American composers writing music like this? Is this how earlier 18th and maybe even 17th century folk/popular music in Britain sounded?
There was quite a bit of influence from the English West Gallery Music , named for the placement of the choir in non-conformist churches in the 18th c. If you search for some examples on YouTube, you'll find it quite similar to American shape note songs of the later 18th; except that the English brought in instruments to double the sung parts. The Congregational Churches of New England felt, like the non-conforming churches of England, that the music should be part of the service sung by the congregation. Usually the small psalm books that were used had simple melodies, and those melodies were often interchangeable- so a congregation could sing a different hymn to a melody they already knew ( this is similar to Broadside ballads, which also typically would have a popular melody named as the tune). By the 1720's, there was a feeling in New England that this simple arrangement had led to very poor music, and two songbooks, John Tufts' Introduction to the Singing of Psalm Tunes and Thomas Walter's The Grounds and Rules of Music Explained were part of a general movement for having part songs and singing schools, and these spread throughout the Colonies- and would later continue to exist in the South.
As composing styles go, it was not inaccessible to a talented amateur like Jeremiah Ingalls. It's contrapuntal, rather than harmonic, so occasional dissonances work fine, creating tensions between the melodic lines- and, like the rhythms, highlighting the words. The harmonies tend to be open, with lots of fifths and octaves and not thirds, triads ( which is why the bass part can be pretty straightforward to sing). Because of the limited harmonies and limited range of pitch, it was also accessible for untrained singers with limited voices, and the shape note system was also a great advantage in this- it meant that someone could learn to sight-read hymns in a few days- so it is not surprising it became popular.
Sacred Harp sings have become quite popular again, no longer done only in singing schools or churches. You can likely find one nearby here
Tony Barrand et. al., Northern Harmony: Plain Tunes, Fuging Tunes and Anthems from the New England Singing School Tradition